69,126 research outputs found
No Generalized TMD-Factorization in the Hadro-Production of High Transverse Momentum Hadrons
It has by now been established that standard QCD factorization using
transverse momentum dependent parton distribution functions fails in
hadro-production of nearly back-to-back hadrons with high transverse momentum.
The essential problem is that gauge invariant transverse momentum dependent
parton distribution functions cannot be defined with process-independent Wilson
line operators, thus implying a breakdown of universality. This has led
naturally to proposals that a correct approach is to instead use a type of
"generalized" transverse momentum dependent factorization in which the basic
factorized structure is assumed to remain valid, but with transverse momentum
dependent parton distribution functions that contain non-standard, process
dependent Wilson line structures. In other words, to recover a factorization
formula, it has become common to assume that it is sufficient to simply modify
the Wilson lines in the parton correlation functions for each separate hadron.
In this paper, we will illustrate by direct counter-example that this is not
possible in a non-Abelian gauge theory. Since a proof of generalized transverse
momentum dependent factorization should apply generally to any hard
hadro-production process, a single counter-example suffices to show that a
general proof does not exist. Therefore, to make the counter-argument clear and
explicit, we illustrate with a specific calculation for a double spin asymmetry
in a spectator model with a non-Abelian gauge field. The observed breakdown of
generalized transverse momentum dependent factorization challenges the notion
that the role of parton transverse momentum in such processes can be described
using separate correlation functions for each external hadron.Comment: 19 pages, 11 figures, typos fixed and minor explanations added,
version to appear in Physical Review
Universality of soft and collinear factors in hard-scattering factorization
Universality in QCD factorization of parton densities, fragmentation
functions, and soft factors is endangered by the process dependence of the
directions of Wilson lines in their definitions. We find a choice of directions
that is consistent with factorization and that gives universality between
e^+e^- annihilation, semi-inclusive deep-inelastic scattering, and the
Drell-Yan process. Universality is only modified by a time-reversal
transformation of the soft function and parton densities between Drell-Yan and
the other processes, whose only effect is the known reversal of sign for T-odd
parton densities like the Sivers function. The modifications of the definitions
needed to remove rapidity divergences with light-like Wilson lines do not
affect the results.Comment: 4 pages. Extra references. Text and references as in published
versio
QCD Factorization for Semi-Inclusive Deep-Inelastic Scattering at Low Transverse Momentum
We demonstrate a factorization formula for semi-inclusive deep-inelastic
scattering with hadrons in the current fragmentation region detected at low
transverse momentum. To facilitate the factorization, we introduce the
transverse-momentum dependent parton distributions and fragmentation functions
with gauge links slightly off the light-cone, and with soft-gluon radiations
subtracted. We verify the factorization to one-loop order in perturbative
quantum chromodynamics and argue that it is valid to all orders in perturbation
theory.Comment: 28 pages, figures include
k_T factorization is violated in production of high-transverse-momentum particles in hadron-hadron collisions
We show that hard-scattering factorization is violated in the production of
high-p_T hadrons in hadron-hadron collisions, in the case that the hadrons are
back-to-back, so that k_T factorization is to be used. The explicit
counterexample that we construct is for the single-spin asymmetry with one beam
transversely polarized. The Sivers function needed here has particular
sensitivity to the Wilson lines in the parton densities. We use a greatly
simplified model theory to make the breakdown of factorization easy to check
explicitly. But the counterexample implies that standard arguments for
factorization fail not just for the single-spin asymmetry but for the
unpolarized cross section for back-to-back hadron production in QCD in
hadron-hadron collisions. This is unlike corresponding cases in e^+e^-
annihilation, Drell-Yan, and deeply inelastic scattering. Moreover, the result
endangers factorization for more general hadroproduction processes.Comment: 10 pages. V. 2: Title change, misprints and minor corrections, as in
journal versio
Demonstration of the Equivalence of Soft and Zero-Bin Subtractions
Calculations of collinear correlation functions in perturbative QCD and
Soft-Collinear Effective Theory (SCET) require a prescription for subtracting
soft or zero-bin contributions in order to avoid double counting the
contributions from soft modes. At leading order in , where
is the SCET expansion parameter, the zero-bin subtractions have been argued to
be equivalent to convolution with soft Wilson lines. We give a proof of the
factorization of naive collinear Wilson lines that is crucial for the
derivation of the equivalence. We then check the equivalence by computing the
non-Abelian two-loop mixed collinear-soft contribution to the jet function in
the quark form factor. These results provide strong support for the
equivalence, which can be used to give a nonperturbative definition of the
zero-bin subtraction at lowest order in .Comment: 14 pages, 3 figure
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